There many operators in Harmonic Analysis which can be described as an average of a family of operators $\{T_j\}_j$ for which some boundedness properties are known. In particular, if $T_j$ are uniformly bounded on $L^p$, then the Minkowski integral inequality tells us that $T$ also satisfies this property. But things change completely if the information that we have is that $T_j$ are of weak type (1,1).

However, under certain condition on the operators $T_j$, the weak type boundedness of $T$ can be reached.

This is a joint work with my student Sergi Baena.

The video of this talk is available on the IISc Math Department channel.